Stink bugs (from the Pentatomidae family) come in a variety of sizes and colors and look like they are wearing armor over their wings. If you've never seen one, you can view more pictures here.
They are commonly called stink bugs because when they are threatened they release an awful smell that protects them from predators. You need to be very careful when getting rid of them as you do not want them to release this scent in your home. The scent won't hurt you, it just smells awful and could attract more stink bugs to the area.
Stink bugs generally live outdoors in yards, gardens, and meadows, but will move indoors looking for warmth and light in the fall and winter months. They can suck the juices from plants in their adult form as well as the nymph form and can do a lot of damage when in high numbers. They especially like fruits and vegetable plants.
They lay their eggs on the underside of leaves on low bushes and wild plants. They cannot reproduce indoors, so that's a bonus for us. The best way to kill them is to gently knock them into a dish of soapy water. Once they have stopped moving, flush them down the toilet. Their armor protects them from many insecticides, so to use them would cause more harm than good in the long run. I don't like to step on them to kill them because this too will release that awful smell.
Stink bugs can flatten themselves out and squeeze through a tiny little area to get into your home. If you are getting a lot of these bugs, or any bugs in your home, then you need to take a serious look at all the areas around your home that could be allowing them access. Common places too look are around windows and vents and all along the seams of your siding. If the problem is minor, some caulk around your windows and doors should do the trick. Make sure there are no holes in your window screens and cover vents with screen whenever possible. Look for large gaps around pipes and under sinks. If you have a huge infestation, you may want to consider having an energy audit done. They will be able to find all the areas where your home is leaking air. Not only will they save on your energy costs, but an added bonus will be no more bugs in your home.
Stinkbugs are attracted to lights, so if you notice that they like to hang out on the side of your house, you may want to look at your lighting set-up. Reduce the amount of lights you have on at night, or reducing their brightness, should help. At night when lights are on inside your home, pull down the shades or use heavy curtains that block light from the outside.
I don't consider these bugs to be a huge pest. They don't bother too many plants in my landscape and some bugs in the Pentatomidae are actually good because they pray on Japanese beetles which are far more destructive then these guys. But I know that in some areas, where populations are higher, these bugs can be a real nuisance.